1 Background

We compare the inference results from TMB, aghq, adam, and tmbstan. Import these inference results as follows:

tmb <- readRDS("depends/tmb.rds")
aghq <- readRDS("depends/aghq.rds")
adam <- readRDS("depends/adam.rds")
adam_time <- adam$time
adam <- adam$adam
tmbstan <- readRDS("depends/tmbstan.rds")

depends <- yaml::read_yaml("orderly.yml")$depends

Check that the parameters (latent field, hyperparameters, model outputs) sampled from each of the four methods are the same:

stopifnot(names(tmb$fit$sample) == names(aghq$quad$sample))
stopifnot(names(tmb$fit$sample) == names(adam$adam$sample))
stopifnot(names(tmb$fit$sample) == names(tmbstan$mcmc$sample))

1.1 Run details

For more information about the conditions under which these results were generated, see:

1.1.1 TMB

dependency_details <- function(i) {
  report_name <- names(depends[[i]])
  print(paste0("Inference results obtained from ", report_name, " with the query ", depends[[i]][[report_name]]$id))
  report_id <- orderly::orderly_search(query = depends[[i]][[report_name]]$id, report_name)
  print(paste0("Obtained report had ID ", report_id, " and was run with the following parameters:"))
  print(orderly::orderly_info(report_id, report_name)$parameters)
}

dependency_details(1)
## [1] "Inference results obtained from naomi-simple_fit with the query latest(parameter:tmb == TRUE && parameter:random_only == TRUE)"
## [1] "Obtained report had ID 20230504-112522-70c6f3bc and was run with the following parameters:"
## $tmb
## [1] TRUE
## 
## $random_only
## [1] TRUE
## 
## $sample
## [1] TRUE
## 
## $aghq
## [1] FALSE
## 
## $k
## [1] 1
## 
## $grid_type
## [1] "product"
## 
## $s
## [1] 1
## 
## $tmbstan
## [1] FALSE
## 
## $hmc_laplace
## [1] FALSE
## 
## $niter
## [1] 1000
## 
## $nthin
## [1] 1
## 
## $adam
## [1] FALSE
## 
## $nsample
## [1] 1000
## 
## $area_level
## [1] 4

1.1.2 aghq

dependency_details(2)
## [1] "Inference results obtained from naomi-simple_fit with the query latest(parameter:aghq == TRUE && parameter:k == 3 && parameter:s == 8)"
## [1] "Obtained report had ID 20230424-192453-b044811f and was run with the following parameters:"
## $aghq
## [1] TRUE
## 
## $k
## [1] 3
## 
## $s
## [1] 8
## 
## $grid_type
## [1] "pca"
## 
## $sample
## [1] TRUE
## 
## $tmb
## [1] FALSE
## 
## $tmbstan
## [1] FALSE
## 
## $hmc_laplace
## [1] FALSE
## 
## $niter
## [1] 1000
## 
## $nthin
## [1] 1
## 
## $adam
## [1] FALSE
## 
## $nsample
## [1] 1000
## 
## $area_level
## [1] 4

1.1.3 adam

dependency_details(3)
## [1] "Inference results obtained from naomi-simple_fit with the query latest(parameter:adam == TRUE)"
## [1] "Obtained report had ID 20230425-190141-a3df2ca3 and was run with the following parameters:"
## $adam
## [1] TRUE
## 
## $sample
## [1] TRUE
## 
## $tmb
## [1] FALSE
## 
## $aghq
## [1] FALSE
## 
## $k
## [1] 1
## 
## $grid_type
## [1] "product"
## 
## $s
## [1] 1
## 
## $tmbstan
## [1] FALSE
## 
## $hmc_laplace
## [1] FALSE
## 
## $niter
## [1] 1000
## 
## $nthin
## [1] 1
## 
## $nsample
## [1] 1000
## 
## $area_level
## [1] 4

1.1.4 tmbstan

tmbstan_details <- dependency_details(4)
## [1] "Inference results obtained from naomi-simple_fit with the query latest(parameter:tmbstan == TRUE && parameter:niter > 50000)"
## [1] "Obtained report had ID 20230414-110613-89cd4244 and was run with the following parameters:"
## $tmbstan
## [1] TRUE
## 
## $niter
## [1] 100000
## 
## $nthin
## [1] 40
## 
## $tmb
## [1] FALSE
## 
## $aghq
## [1] FALSE
## 
## $k
## [1] 1
## 
## $grid_type
## [1] "product"
## 
## $s
## [1] 1
## 
## $hmc_laplace
## [1] FALSE
## 
## $adam
## [1] FALSE
## 
## $nsample
## [1] 5000
## 
## $area_level
## [1] 4
tmbstan_details
## $tmbstan
## [1] TRUE
## 
## $niter
## [1] 100000
## 
## $nthin
## [1] 40
## 
## $tmb
## [1] FALSE
## 
## $aghq
## [1] FALSE
## 
## $k
## [1] 1
## 
## $grid_type
## [1] "product"
## 
## $s
## [1] 1
## 
## $hmc_laplace
## [1] FALSE
## 
## $adam
## [1] FALSE
## 
## $nsample
## [1] 5000
## 
## $area_level
## [1] 4

1.2 Time taken

time_taken <- data.frame(
  "TMB" = tmb$time,
  "aghq" = aghq$time,
  "adam" = adam_time,
  "tmbstan" = tmbstan$time
)

write_csv(time_taken, "time_taken.csv")

time_taken

2 Histograms and ECDF difference plots

We create histograms and empirical cumulative distribution function (ECDF) difference plots of the samples from each method. All of the possible latent field and hyperparamter names are given by pars:

pars <- names(tmb$fit$sample)

There are also all of the Naomi outcome variables:

names(tmb$fit$sample)[!(names(tmb$fit$sample) %in% unique(names(tmb$fit$obj$env$par)))]
##  [1] "anc_clients_t1_out"            "population_t1_out"             "plhiv_attend_t1_out"           "anc_already_art_t1_out"       
##  [5] "anc_tested_pos_t1_out"         "anc_tested_neg_t1_out"         "anc_rho_obs_t1_ll"             "hhs_prev_ll"                  
##  [9] "u_rho_xa"                      "anc_art_new_t1_out"            "untreated_plhiv_attend_t1_out" "untreated_plhiv_num_t1_out"   
## [13] "artattend_ij_t1_out"           "anc_known_pos_t1_out"          "artattend_t1_out"              "rho_t1_out"                   
## [17] "anc_rho_t1_out"                "artnum_t1_out"                 "anc_alpha_t1_out"              "alpha_t1_out"                 
## [21] "infections_t1_out"             "anc_plhiv_t1_out"              "plhiv_t1_out"                  "lambda_t1_out"                
## [25] "hhs_artcov_ll"                 "artnum_t1_ll"

We will especially focus on the outputs:

  • HIV prevalence (rho_t1_out) which has 6417 variables (rows)
  • ART coverage (alpha_t1_out) which has 6417 variables (rows)
  • HIV incidence (lambda_t1_out) which has 6417 variables (rows)

These outputs are at an aggregate resolution as well as at the finest resolution. It seems to make sense to only to assess inferential accuracy at the finest resolution so as to avoid double counting. As such, we need to find the subset of these variables at the finest resolution. Within tmb$naomi_data there is a dataframe called mf_out (model frame output) which contains the area, age, sex mapping for these 6417 rows. As a sanity check, confirm that the number of areas times number of ages times number of sexes indeed equals the number of rows:

mf_out <- tmb$naomi_data$mf_out
(n_area <- length(unique(mf_out$area_id)))
## [1] 69
(n_age <- length(unique(mf_out$age_group)))
## [1] 31
(n_sex <- length(unique(mf_out$sex)))
## [1] 3
stopifnot(n_area * n_age * n_sex == dim(tmb$fit$sample$rho_t1_out)[1])

The unique levels for area, age and sex are:

mf_out$area_id %>% unique()
##  [1] "MWI"           "MWI_1_1_demo"  "MWI_1_2_demo"  "MWI_1_3_demo"  "MWI_2_1_demo"  "MWI_2_2_demo"  "MWI_2_3_demo"  "MWI_2_4_demo" 
##  [9] "MWI_2_5_demo"  "MWI_3_1_demo"  "MWI_3_10_demo" "MWI_3_11_demo" "MWI_3_12_demo" "MWI_3_13_demo" "MWI_3_14_demo" "MWI_3_15_demo"
## [17] "MWI_3_16_demo" "MWI_3_17_demo" "MWI_3_18_demo" "MWI_3_19_demo" "MWI_3_2_demo"  "MWI_3_20_demo" "MWI_3_21_demo" "MWI_3_22_demo"
## [25] "MWI_3_23_demo" "MWI_3_24_demo" "MWI_3_25_demo" "MWI_3_26_demo" "MWI_3_27_demo" "MWI_3_28_demo" "MWI_3_3_demo"  "MWI_3_4_demo" 
## [33] "MWI_3_5_demo"  "MWI_3_6_demo"  "MWI_3_7_demo"  "MWI_3_8_demo"  "MWI_3_9_demo"  "MWI_4_1_demo"  "MWI_4_10_demo" "MWI_4_11_demo"
## [41] "MWI_4_12_demo" "MWI_4_13_demo" "MWI_4_14_demo" "MWI_4_15_demo" "MWI_4_16_demo" "MWI_4_17_demo" "MWI_4_18_demo" "MWI_4_19_demo"
## [49] "MWI_4_2_demo"  "MWI_4_20_demo" "MWI_4_21_demo" "MWI_4_22_demo" "MWI_4_23_demo" "MWI_4_24_demo" "MWI_4_25_demo" "MWI_4_26_demo"
## [57] "MWI_4_27_demo" "MWI_4_28_demo" "MWI_4_29_demo" "MWI_4_3_demo"  "MWI_4_30_demo" "MWI_4_31_demo" "MWI_4_32_demo" "MWI_4_4_demo" 
## [65] "MWI_4_5_demo"  "MWI_4_6_demo"  "MWI_4_7_demo"  "MWI_4_8_demo"  "MWI_4_9_demo"
mf_out$age_group %>% unique()
##  [1] "Y000_004" "Y000_014" "Y000_064" "Y000_999" "Y005_009" "Y010_014" "Y010_019" "Y015_019" "Y015_024" "Y015_049" "Y015_064" "Y015_999"
## [13] "Y020_024" "Y025_029" "Y025_034" "Y025_049" "Y030_034" "Y035_039" "Y035_049" "Y040_044" "Y045_049" "Y050_054" "Y050_064" "Y050_999"
## [25] "Y055_059" "Y060_064" "Y065_069" "Y065_999" "Y070_074" "Y075_079" "Y080_999"
mf_out$sex %>% unique()
## [1] "both"   "female" "male"

Filter to only the finest resolution, adding an id column has to enable merging to the samples:

mf_out_fine <- mf_out %>%
  tibble::rownames_to_column("id") %>%
  mutate(id = as.numeric(id)) %>%
  filter(
    area_id %in% paste0("MWI_4_", 1:32, "_demo"),
    sex %in% c("male", "female"),
    age_group %in%
      c(
        "Y000_004", "Y005_009", "Y010_014", "Y015_019", "Y020_024", "Y025_029",
        "Y025_034", "Y030_034", "Y035_039", "Y040_044", "Y045_049", "Y050_054",
        "Y055_059", "Y060_064", "Y065_069", "Y070_074", "Y075_079", "Y080_999"
      )
  )

We will produce plots about the a small subset of parameters for the time being. There is no particular reason to choose this subset rather than other, it’s quite arbitrary.

pars_eval <- pars %in% c("beta_rho", "u_rho_x")
names(pars_eval) <- pars
histogram_and_ecdf_helper <- function(par) lapply(1:sum(names(tmb$fit$obj$env$par) == par), histogram_and_ecdf, par = par)

2.1 beta_rho

histogram_and_ecdf_helper("beta_rho")
## [[1]]

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2.2 beta_alpha

histogram_and_ecdf_helper("beta_alpha")
## [[1]]

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2.3 beta_lambda

histogram_and_ecdf_helper("beta_lambda")
## [[1]]

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2.4 beta_anc_rho

histogram_and_ecdf("beta_anc_rho")

2.5 beta_anc_alpha

histogram_and_ecdf("beta_anc_alpha")

2.6 logit

lapply(pars[stringr::str_starts(pars, "logit")], histogram_and_ecdf)

2.7 log_sigma

lapply(pars[stringr::str_starts(pars, "log_sigma")], histogram_and_ecdf)

2.8 u_rho_x

histogram_and_ecdf_helper("u_rho_x")
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2.9 us_rho_x

histogram_and_ecdf_helper("us_rho_x")

2.10 u_rho_xs

histogram_and_ecdf_helper("u_rho_xs")

2.11 us_rho_xs

histogram_and_ecdf_helper("us_rho_xs")

2.12 u_rho_as

histogram_and_ecdf_helper("u_rho_as")

2.13 u_alpha_x

histogram_and_ecdf_helper("u_alpha_x")

2.14 us_alpha_x

histogram_and_ecdf_helper("us_alpha_x")

2.15 u_alpha_xs

histogram_and_ecdf_helper("u_alpha_xs")

2.16 us_alpha_xs

histogram_and_ecdf_helper("us_alpha_xs")
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2.17 u_alpha_a

histogram_and_ecdf_helper("u_alpha_a")

2.18 u_alpha_as

histogram_and_ecdf_helper("u_alpha_as")

2.19 u_alpha_xa

histogram_and_ecdf_helper("u_alpha_xa")

2.20 ui_lambda_x

histogram_and_ecdf_helper("ui_lambda_x")

2.21 ui_anc_rho_x

histogram_and_ecdf_helper("ui_anc_rho_x")

2.22 ui_anc_alpha_x

histogram_and_ecdf_helper("ui_anc_alpha_x")

2.23 log_or_gamma

histogram_and_ecdf_helper("log_or_gamma")

2.24 rho_t1_out

There are too many variables to plot this here!

2.25 alpha_t1_out

There are too many variables to plot this here!

2.26 lambda_t1_out

There are too many variables to plot this here!

3 KS plots

3.1 Individual parameters

ks_helper <- function(par, starts_with = FALSE, ...) {
  to_ks_df(par, starts_with = starts_with) %>% ks_plot(par, ...)
}

ks_df_out <- function(par) {
  to_ks_df(par = par, outputs = TRUE, id = mf_out_fine$id) %>%
  select(-par) %>%
  left_join(
    mf_out_fine %>%
      rename("full_id" = "id") %>%
      tibble::rowid_to_column("index") %>%
      mutate(index = as.numeric(index))
  )
}

3.1.1 beta

ks_helper("beta", starts_with = TRUE)

3.1.2 logit

ks_helper("logit", starts_with = TRUE)

3.1.3 log_sigma

ks_helper("log_sigma", starts_with = TRUE)

3.1.4 u_rho_x

ks_helper("u_rho_x")

3.1.5 u_rho_xs

ks_helper("u_rho_xs")

3.1.6 us_rho_x

ks_helper("us_rho_x")

3.1.7 us_rho_xs

ks_helper("us_rho_xs")

3.1.8 u_rho_a

ks_helper("u_rho_a")

3.1.9 u_rho_as

ks_helper("u_rho_as")

3.1.10 u_alpha_x

ks_helper("u_alpha_x")

3.1.11 u_alpha_xs

ks_helper("u_alpha_xs")

3.1.12 us_alpha_x

ks_helper("us_alpha_x")

3.1.13 us_alpha_xs

ks_helper("us_alpha_xs")

3.1.14 u_alpha_a

ks_helper("u_alpha_a")

3.1.15 u_alpha_as

ks_helper("u_alpha_as")

3.1.16 u_alpha_xa

ks_helper("u_alpha_xa")

3.1.17 ui_anc_rho_x

ks_helper("ui_anc_rho_x")

3.1.18 ui_anc_alpha_x

ks_helper("ui_anc_alpha_x")

3.1.19 log_or_gamma

ks_helper("log_or_gamma")

3.1.20 rho_t1_out

ks_df_out(par = "rho_t1_out") %>%
  ks_plot(par = "rho_t1_out", alpha = 0.2)
## Joining, by = "index"

3.1.21 alpha_t1_out

ks_df_out(par = "alpha_t1_out") %>%
  ks_plot(par = "rho_t1_out", alpha = 0.2)
## Joining, by = "index"

3.1.22 lambda_t1_out

ks_df_out(par = "rho_t1_out") %>%
  filter(!age_group %in% c("Y005_009", "Y010_014", "Y080_999")) %>%
  ks_plot(par = "lambda_t1_out", alpha = 0.2)
## Joining, by = "index"

Filter out the age group 5-9, 10-14 and 80+ here becausethere are new new infections in those age groups, and the posterior samples from each method are exactly the same: in particular draws of identically zero.

ks_lambda_t1_out %>%
  filter(ks == 0) %>%
  group_by(method) %>%
  summarise(n = n())
ks_lambda_t1_out %>%
  filter(ks == 0) %>%
  pull(age_group) %>%
  unique()
## [1] "Y005_009" "Y010_014" "Y080_999"

3.2 Summary

Values in dark blue are the lowest KS difference for that particular parameter:

options(dplyr.summarise.inform = FALSE)

ks_summary <- lapply(unique(names(tmb$fit$obj$env$par)), function(x) {
  to_ks_df(x) %>%
    group_by(method, index) %>%
    summarise(ks = mean(ks), par = x) %>%
    ungroup()
}) %>%
  bind_rows() %>%
  pivot_wider(names_from = "method", values_from = "ks") %>%
  rename(
    "Parameter" = "par",
    "KS(adam, tmbstan)" = "adam",
    "KS(aghq, tmbstan)" = "aghq",
    "KS(TMB, tmbstan)" = "TMB",
  )

r <- adam$quad$obj$env$random
x_names <- names(adam$quad$obj$env$par[r])
theta_names <- names(adam$quad$obj$env$par[-r])

dict <- data.frame(
  Parameter = c(unique(x_names), unique(theta_names)),
  Type = c(rep("Latent field", length(unique(x_names))), rep("Hyper", length(unique(theta_names))))
)

ks_summary <- ks_summary %>%
  left_join(dict, by = "Parameter")

saveRDS(ks_summary_out, "ks_summary_out.rds")

ks_summary %>%
  filter(Type != "Hyper") %>%
  ks_plot_many("TMB", "aghq")
## Warning: Removed 116 rows containing missing values (`geom_tile()`).
## Picking joint bandwidth of 0.0064

(ks_summary_out <- ks_summary %>%
  group_by(Type) %>%
  summarise(
    TMB = mean(`KS(TMB, tmbstan)`),
    aghq = mean(`KS(aghq, tmbstan)`),
    adam = mean(`KS(adam, tmbstan)`)
  )) %>%
  gt::gt()
Type TMB aghq adam
Hyper 0.56757500 0.56767500 0.56767500
Latent field 0.08443169 0.07512077 0.08234904

3.2.1 Latent field

ks_table(ks_summary, type = "Latent field")
index Parameter KS(adam, tmbstan) KS(aghq, tmbstan) KS(TMB, tmbstan) Type
1 beta_rho 0.073 0.080 0.071 Latent field
2 beta_rho 0.074 0.065 0.066 Latent field
1 beta_alpha 0.069 0.040 0.079 Latent field
2 beta_alpha 0.111 0.111 0.115 Latent field
1 beta_lambda 0.031 0.095 0.128 Latent field
2 beta_lambda 0.023 0.046 0.026 Latent field
1 beta_anc_rho 0.032 0.113 0.138 Latent field
1 beta_anc_alpha 0.084 0.077 0.093 Latent field
1 u_rho_x 0.050 0.055 0.051 Latent field
2 u_rho_x 0.041 0.105 0.060 Latent field
3 u_rho_x 0.031 0.020 0.034 Latent field
4 u_rho_x 0.037 0.090 0.065 Latent field
5 u_rho_x 0.125 0.062 0.115 Latent field
6 u_rho_x 0.125 0.152 0.136 Latent field
7 u_rho_x 0.084 0.157 0.157 Latent field
8 u_rho_x 0.059 0.041 0.030 Latent field
9 u_rho_x 0.042 0.067 0.030 Latent field
10 u_rho_x 0.052 0.082 0.084 Latent field
11 u_rho_x 0.062 0.045 0.042 Latent field
12 u_rho_x 0.116 0.149 0.164 Latent field
13 u_rho_x 0.038 0.050 0.056 Latent field
14 u_rho_x 0.094 0.086 0.104 Latent field
15 u_rho_x 0.058 0.019 0.038 Latent field
16 u_rho_x 0.045 0.031 0.035 Latent field
17 u_rho_x 0.020 0.031 0.060 Latent field
18 u_rho_x 0.063 0.031 0.045 Latent field
19 u_rho_x 0.097 0.044 0.065 Latent field
20 u_rho_x 0.038 0.023 0.032 Latent field
21 u_rho_x 0.045 0.096 0.081 Latent field
22 u_rho_x 0.164 0.131 0.149 Latent field
23 u_rho_x 0.057 0.038 0.039 Latent field
24 u_rho_x 0.105 0.036 0.046 Latent field
25 u_rho_x 0.045 0.062 0.048 Latent field
26 u_rho_x 0.065 0.033 0.055 Latent field
27 u_rho_x 0.099 0.099 0.070 Latent field
28 u_rho_x 0.030 0.034 0.024 Latent field
29 u_rho_x 0.072 0.087 0.116 Latent field
30 u_rho_x 0.070 0.042 0.045 Latent field
31 u_rho_x 0.067 0.048 0.066 Latent field
32 u_rho_x 0.035 0.092 0.083 Latent field
1 us_rho_x 0.134 0.170 0.174 Latent field
2 us_rho_x 0.135 0.107 0.130 Latent field
3 us_rho_x 0.106 0.084 0.110 Latent field
4 us_rho_x 0.105 0.082 0.072 Latent field
5 us_rho_x 0.079 0.067 0.058 Latent field
6 us_rho_x 0.203 0.194 0.180 Latent field
7 us_rho_x 0.057 0.061 0.033 Latent field
8 us_rho_x 0.075 0.068 0.087 Latent field
9 us_rho_x 0.070 0.055 0.035 Latent field
10 us_rho_x 0.062 0.073 0.051 Latent field
11 us_rho_x 0.088 0.085 0.074 Latent field
12 us_rho_x 0.109 0.087 0.111 Latent field
13 us_rho_x 0.073 0.054 0.062 Latent field
14 us_rho_x 0.057 0.085 0.042 Latent field
15 us_rho_x 0.057 0.070 0.067 Latent field
16 us_rho_x 0.062 0.081 0.113 Latent field
17 us_rho_x 0.040 0.058 0.089 Latent field
18 us_rho_x 0.110 0.114 0.114 Latent field
19 us_rho_x 0.062 0.127 0.032 Latent field
20 us_rho_x 0.106 0.138 0.116 Latent field
21 us_rho_x 0.096 0.085 0.095 Latent field
22 us_rho_x 0.114 0.075 0.099 Latent field
23 us_rho_x 0.092 0.072 0.054 Latent field
24 us_rho_x 0.035 0.037 0.068 Latent field
25 us_rho_x 0.062 0.098 0.074 Latent field
26 us_rho_x 0.079 0.080 0.103 Latent field
27 us_rho_x 0.052 0.031 0.033 Latent field
28 us_rho_x 0.059 0.043 0.052 Latent field
29 us_rho_x 0.072 0.108 0.087 Latent field
30 us_rho_x 0.084 0.066 0.070 Latent field
31 us_rho_x 0.051 0.058 0.043 Latent field
32 us_rho_x 0.109 0.040 0.066 Latent field
1 u_rho_xs 0.128 0.080 0.078 Latent field
2 u_rho_xs 0.087 0.111 0.094 Latent field
3 u_rho_xs 0.112 0.123 0.120 Latent field
4 u_rho_xs 0.119 0.104 0.121 Latent field
5 u_rho_xs 0.193 0.163 0.203 Latent field
6 u_rho_xs 0.268 0.227 0.266 Latent field
7 u_rho_xs 0.190 0.200 0.202 Latent field
8 u_rho_xs 0.107 0.107 0.106 Latent field
9 u_rho_xs 0.123 0.139 0.124 Latent field
10 u_rho_xs 0.084 0.078 0.097 Latent field
11 u_rho_xs 0.105 0.098 0.099 Latent field
12 u_rho_xs 0.246 0.204 0.241 Latent field
13 u_rho_xs 0.104 0.135 0.146 Latent field
14 u_rho_xs 0.138 0.136 0.171 Latent field
15 u_rho_xs 0.159 0.151 0.176 Latent field
16 u_rho_xs 0.103 0.104 0.123 Latent field
17 u_rho_xs 0.102 0.095 0.118 Latent field
18 u_rho_xs 0.187 0.145 0.191 Latent field
19 u_rho_xs 0.172 0.150 0.193 Latent field
20 u_rho_xs 0.130 0.101 0.117 Latent field
21 u_rho_xs 0.110 0.127 0.137 Latent field
22 u_rho_xs 0.262 0.234 0.268 Latent field
23 u_rho_xs 0.165 0.167 0.163 Latent field
24 u_rho_xs 0.211 0.185 0.196 Latent field
25 u_rho_xs 0.115 0.100 0.115 Latent field
26 u_rho_xs 0.146 0.146 0.135 Latent field
27 u_rho_xs 0.205 0.177 0.215 Latent field
28 u_rho_xs 0.139 0.118 0.110 Latent field
29 u_rho_xs 0.203 0.173 0.203 Latent field
30 u_rho_xs 0.144 0.120 0.117 Latent field
31 u_rho_xs 0.155 0.135 0.163 Latent field
32 u_rho_xs 0.135 0.124 0.093 Latent field
1 us_rho_xs 0.036 0.036 0.029 Latent field
2 us_rho_xs 0.023 0.024 0.039 Latent field
3 us_rho_xs 0.027 0.031 0.046 Latent field
4 us_rho_xs 0.016 0.035 0.023 Latent field
5 us_rho_xs 0.044 0.045 0.051 Latent field
6 us_rho_xs 0.034 0.056 0.021 Latent field
7 us_rho_xs 0.077 0.060 0.050 Latent field
8 us_rho_xs 0.035 0.049 0.026 Latent field
9 us_rho_xs 0.028 0.039 0.037 Latent field
10 us_rho_xs 0.051 0.024 0.021 Latent field
11 us_rho_xs 0.026 0.037 0.057 Latent field
12 us_rho_xs 0.052 0.050 0.037 Latent field
13 us_rho_xs 0.040 0.039 0.031 Latent field
14 us_rho_xs 0.022 0.028 0.033 Latent field
15 us_rho_xs 0.032 0.056 0.034 Latent field
16 us_rho_xs 0.021 0.050 0.020 Latent field
17 us_rho_xs 0.027 0.025 0.021 Latent field
18 us_rho_xs 0.030 0.037 0.032 Latent field
19 us_rho_xs 0.041 0.044 0.023 Latent field
20 us_rho_xs 0.030 0.044 0.036 Latent field
21 us_rho_xs 0.041 0.027 0.024 Latent field
22 us_rho_xs 0.040 0.039 0.025 Latent field
23 us_rho_xs 0.045 0.042 0.023 Latent field
24 us_rho_xs 0.038 0.038 0.035 Latent field
25 us_rho_xs 0.076 0.049 0.051 Latent field
26 us_rho_xs 0.043 0.040 0.036 Latent field
27 us_rho_xs 0.047 0.022 0.049 Latent field
28 us_rho_xs 0.041 0.036 0.025 Latent field
29 us_rho_xs 0.031 0.051 0.020 Latent field
30 us_rho_xs 0.053 0.032 0.037 Latent field
31 us_rho_xs 0.042 0.045 0.058 Latent field
32 us_rho_xs 0.031 0.031 0.028 Latent field
1 u_rho_a 0.075 0.077 0.072 Latent field
2 u_rho_a 0.074 0.084 0.076 Latent field
3 u_rho_a 0.069 0.084 0.075 Latent field
4 u_rho_a 0.081 0.082 0.072 Latent field
5 u_rho_a 0.069 0.084 0.070 Latent field
6 u_rho_a 0.086 0.082 0.070 Latent field
7 u_rho_a 0.070 0.090 0.072 Latent field
8 u_rho_a 0.073 0.080 0.077 Latent field
9 u_rho_a 0.081 0.078 0.070 Latent field
10 u_rho_a 0.080 0.087 0.070 Latent field
1 u_rho_as 0.072 0.041 0.067 Latent field
2 u_rho_as 0.072 0.063 0.066 Latent field
3 u_rho_as 0.072 0.059 0.065 Latent field
4 u_rho_as 0.078 0.064 0.067 Latent field
5 u_rho_as 0.065 0.061 0.070 Latent field
6 u_rho_as 0.069 0.060 0.066 Latent field
7 u_rho_as 0.071 0.056 0.065 Latent field
8 u_rho_as 0.060 0.061 0.064 Latent field
9 u_rho_as 0.072 0.080 0.065 Latent field
10 u_rho_as 0.078 0.085 0.071 Latent field
1 u_alpha_x 0.122 0.120 0.157 Latent field
2 u_alpha_x 0.126 0.111 0.158 Latent field
3 u_alpha_x 0.114 0.095 0.140 Latent field
4 u_alpha_x 0.142 0.137 0.131 Latent field
5 u_alpha_x 0.139 0.109 0.124 Latent field
6 u_alpha_x 0.104 0.083 0.076 Latent field
7 u_alpha_x 0.107 0.059 0.058 Latent field
8 u_alpha_x 0.177 0.135 0.157 Latent field
9 u_alpha_x 0.161 0.129 0.179 Latent field
10 u_alpha_x 0.185 0.132 0.169 Latent field
11 u_alpha_x 0.154 0.113 0.154 Latent field
12 u_alpha_x 0.116 0.056 0.072 Latent field
13 u_alpha_x 0.158 0.093 0.146 Latent field
14 u_alpha_x 0.087 0.047 0.102 Latent field
15 u_alpha_x 0.099 0.073 0.112 Latent field
16 u_alpha_x 0.059 0.058 0.047 Latent field
17 u_alpha_x 0.090 0.092 0.130 Latent field
18 u_alpha_x 0.123 0.140 0.134 Latent field
19 u_alpha_x 0.112 0.117 0.124 Latent field
20 u_alpha_x 0.118 0.109 0.096 Latent field
21 u_alpha_x 0.171 0.148 0.173 Latent field
22 u_alpha_x 0.119 0.116 0.159 Latent field
23 u_alpha_x 0.134 0.119 0.123 Latent field
24 u_alpha_x 0.133 0.081 0.134 Latent field
25 u_alpha_x 0.099 0.089 0.130 Latent field
26 u_alpha_x 0.117 0.071 0.133 Latent field
27 u_alpha_x 0.131 0.132 0.148 Latent field
28 u_alpha_x 0.091 0.078 0.112 Latent field
29 u_alpha_x 0.098 0.097 0.096 Latent field
30 u_alpha_x 0.109 0.087 0.141 Latent field
31 u_alpha_x 0.086 0.052 0.102 Latent field
32 u_alpha_x 0.069 0.061 0.064 Latent field
1 us_alpha_x 0.069 0.076 0.095 Latent field
2 us_alpha_x 0.070 0.062 0.079 Latent field
3 us_alpha_x 0.085 0.066 0.095 Latent field
4 us_alpha_x 0.066 0.068 0.079 Latent field
5 us_alpha_x 0.107 0.067 0.099 Latent field
6 us_alpha_x 0.094 0.063 0.089 Latent field
7 us_alpha_x 0.025 0.026 0.027 Latent field
8 us_alpha_x 0.144 0.070 0.110 Latent field
9 us_alpha_x 0.135 0.075 0.122 Latent field
10 us_alpha_x 0.131 0.067 0.104 Latent field
11 us_alpha_x 0.103 0.057 0.099 Latent field
12 us_alpha_x 0.098 0.048 0.067 Latent field
13 us_alpha_x 0.103 0.061 0.098 Latent field
14 us_alpha_x 0.064 0.051 0.072 Latent field
15 us_alpha_x 0.087 0.050 0.093 Latent field
16 us_alpha_x 0.043 0.035 0.022 Latent field
17 us_alpha_x 0.092 0.065 0.092 Latent field
18 us_alpha_x 0.084 0.076 0.074 Latent field
19 us_alpha_x 0.084 0.073 0.095 Latent field
20 us_alpha_x 0.083 0.074 0.087 Latent field
21 us_alpha_x 0.131 0.083 0.100 Latent field
22 us_alpha_x 0.184 0.106 0.169 Latent field
23 us_alpha_x 0.084 0.077 0.109 Latent field
24 us_alpha_x 0.103 0.064 0.116 Latent field
25 us_alpha_x 0.102 0.061 0.104 Latent field
26 us_alpha_x 0.074 0.061 0.089 Latent field
27 us_alpha_x 0.077 0.057 0.092 Latent field
28 us_alpha_x 0.066 0.047 0.072 Latent field
29 us_alpha_x 0.106 0.086 0.122 Latent field
30 us_alpha_x 0.072 0.040 0.091 Latent field
31 us_alpha_x 0.051 0.035 0.076 Latent field
32 us_alpha_x 0.041 0.030 0.057 Latent field
1 u_alpha_xs 0.034 0.069 0.054 Latent field
2 u_alpha_xs 0.069 0.066 0.071 Latent field
3 u_alpha_xs 0.034 0.073 0.057 Latent field
4 u_alpha_xs 0.132 0.138 0.109 Latent field
5 u_alpha_xs 0.128 0.050 0.077 Latent field
6 u_alpha_xs 0.033 0.043 0.028 Latent field
7 u_alpha_xs 0.051 0.057 0.073 Latent field
8 u_alpha_xs 0.068 0.067 0.079 Latent field
9 u_alpha_xs 0.085 0.059 0.073 Latent field
10 u_alpha_xs 0.096 0.084 0.143 Latent field
11 u_alpha_xs 0.129 0.080 0.116 Latent field
12 u_alpha_xs 0.107 0.094 0.127 Latent field
13 u_alpha_xs 0.104 0.043 0.106 Latent field
14 u_alpha_xs 0.049 0.076 0.054 Latent field
15 u_alpha_xs 0.106 0.103 0.166 Latent field
16 u_alpha_xs 0.123 0.103 0.136 Latent field
17 u_alpha_xs 0.085 0.063 0.060 Latent field
18 u_alpha_xs 0.148 0.161 0.142 Latent field
19 u_alpha_xs 0.059 0.053 0.049 Latent field
20 u_alpha_xs 0.047 0.051 0.062 Latent field
21 u_alpha_xs 0.086 0.079 0.081 Latent field
22 u_alpha_xs 0.166 0.120 0.131 Latent field
23 u_alpha_xs 0.089 0.070 0.097 Latent field
24 u_alpha_xs 0.133 0.100 0.125 Latent field
25 u_alpha_xs 0.155 0.101 0.101 Latent field
26 u_alpha_xs 0.064 0.052 0.059 Latent field
27 u_alpha_xs 0.119 0.126 0.130 Latent field
28 u_alpha_xs 0.083 0.036 0.042 Latent field
29 u_alpha_xs 0.173 0.121 0.162 Latent field
30 u_alpha_xs 0.095 0.078 0.109 Latent field
31 u_alpha_xs 0.117 0.054 0.113 Latent field
32 u_alpha_xs 0.119 0.065 0.116 Latent field
1 us_alpha_xs 0.042 0.038 0.058 Latent field
2 us_alpha_xs 0.032 0.068 0.048 Latent field
3 us_alpha_xs 0.049 0.034 0.042 Latent field
4 us_alpha_xs 0.058 0.070 0.079 Latent field
5 us_alpha_xs 0.070 0.070 0.060 Latent field
6 us_alpha_xs 0.061 0.071 0.064 Latent field
7 us_alpha_xs 0.034 0.032 0.025 Latent field
8 us_alpha_xs 0.093 0.057 0.103 Latent field
9 us_alpha_xs 0.100 0.065 0.110 Latent field
10 us_alpha_xs 0.114 0.070 0.120 Latent field
11 us_alpha_xs 0.101 0.091 0.123 Latent field
12 us_alpha_xs 0.098 0.089 0.124 Latent field
13 us_alpha_xs 0.116 0.053 0.089 Latent field
14 us_alpha_xs 0.069 0.033 0.072 Latent field
15 us_alpha_xs 0.110 0.091 0.140 Latent field
16 us_alpha_xs 0.142 0.061 0.116 Latent field
17 us_alpha_xs 0.082 0.024 0.073 Latent field
18 us_alpha_xs 0.111 0.027 0.099 Latent field
19 us_alpha_xs 0.037 0.056 0.025 Latent field
20 us_alpha_xs 0.034 0.045 0.035 Latent field
21 us_alpha_xs 0.070 0.026 0.072 Latent field
22 us_alpha_xs 0.096 0.090 0.102 Latent field
23 us_alpha_xs 0.125 0.064 0.123 Latent field
24 us_alpha_xs 0.150 0.082 0.124 Latent field
25 us_alpha_xs 0.084 0.070 0.078 Latent field
26 us_alpha_xs 0.155 0.084 0.132 Latent field
27 us_alpha_xs 0.141 0.079 0.129 Latent field
28 us_alpha_xs 0.115 0.073 0.095 Latent field
29 us_alpha_xs 0.137 0.079 0.138 Latent field
30 us_alpha_xs 0.166 0.085 0.154 Latent field
31 us_alpha_xs 0.130 0.072 0.122 Latent field
32 us_alpha_xs 0.140 0.070 0.123 Latent field
1 u_alpha_a 0.055 0.033 0.070 Latent field
2 u_alpha_a 0.069 0.036 0.078 Latent field
3 u_alpha_a 0.066 0.031 0.070 Latent field
4 u_alpha_a 0.052 0.035 0.074 Latent field
5 u_alpha_a 0.073 0.037 0.078 Latent field
6 u_alpha_a 0.060 0.025 0.072 Latent field
7 u_alpha_a 0.069 0.023 0.076 Latent field
8 u_alpha_a 0.068 0.030 0.073 Latent field
9 u_alpha_a 0.065 0.042 0.073 Latent field
10 u_alpha_a 0.064 0.036 0.068 Latent field
11 u_alpha_a 0.075 0.034 0.070 Latent field
12 u_alpha_a 0.067 0.044 0.075 Latent field
13 u_alpha_a 0.066 0.042 0.068 Latent field
1 u_alpha_as 0.067 0.094 0.081 Latent field
2 u_alpha_as 0.100 0.103 0.106 Latent field
3 u_alpha_as 0.120 0.104 0.131 Latent field
4 u_alpha_as 0.129 0.104 0.107 Latent field
5 u_alpha_as 0.155 0.103 0.119 Latent field
6 u_alpha_as 0.094 0.074 0.095 Latent field
7 u_alpha_as 0.077 0.067 0.077 Latent field
8 u_alpha_as 0.060 0.057 0.060 Latent field
9 u_alpha_as 0.059 0.040 0.058 Latent field
10 u_alpha_as 0.064 0.044 0.063 Latent field
1 u_alpha_xa 0.033 0.056 0.051 Latent field
2 u_alpha_xa 0.067 0.039 0.040 Latent field
3 u_alpha_xa 0.058 0.036 0.039 Latent field
4 u_alpha_xa 0.080 0.063 0.072 Latent field
5 u_alpha_xa 0.109 0.074 0.103 Latent field
6 u_alpha_xa 0.109 0.122 0.100 Latent field
7 u_alpha_xa 0.081 0.088 0.090 Latent field
8 u_alpha_xa 0.061 0.048 0.081 Latent field
9 u_alpha_xa 0.069 0.037 0.053 Latent field
10 u_alpha_xa 0.103 0.092 0.161 Latent field
11 u_alpha_xa 0.094 0.086 0.122 Latent field
12 u_alpha_xa 0.116 0.068 0.121 Latent field
13 u_alpha_xa 0.073 0.017 0.083 Latent field
14 u_alpha_xa 0.084 0.094 0.095 Latent field
15 u_alpha_xa 0.054 0.043 0.062 Latent field
16 u_alpha_xa 0.038 0.052 0.048 Latent field
17 u_alpha_xa 0.046 0.032 0.026 Latent field
18 u_alpha_xa 0.038 0.037 0.033 Latent field
19 u_alpha_xa 0.098 0.053 0.090 Latent field
20 u_alpha_xa 0.042 0.039 0.054 Latent field
21 u_alpha_xa 0.082 0.077 0.105 Latent field
22 u_alpha_xa 0.218 0.184 0.220 Latent field
23 u_alpha_xa 0.024 0.037 0.051 Latent field
24 u_alpha_xa 0.061 0.020 0.055 Latent field
25 u_alpha_xa 0.091 0.063 0.057 Latent field
26 u_alpha_xa 0.033 0.053 0.020 Latent field
27 u_alpha_xa 0.097 0.122 0.104 Latent field
28 u_alpha_xa 0.069 0.045 0.046 Latent field
29 u_alpha_xa 0.035 0.050 0.053 Latent field
30 u_alpha_xa 0.058 0.062 0.060 Latent field
31 u_alpha_xa 0.026 0.035 0.044 Latent field
32 u_alpha_xa 0.038 0.027 0.054 Latent field
1 ui_lambda_x 0.112 0.124 0.119 Latent field
2 ui_lambda_x 0.123 0.121 0.126 Latent field
3 ui_lambda_x 0.101 0.126 0.108 Latent field
4 ui_lambda_x 0.108 0.121 0.129 Latent field
5 ui_lambda_x 0.124 0.101 0.114 Latent field
6 ui_lambda_x 0.093 0.092 0.087 Latent field
7 ui_lambda_x 0.114 0.136 0.109 Latent field
8 ui_lambda_x 0.115 0.119 0.102 Latent field
9 ui_lambda_x 0.117 0.097 0.105 Latent field
10 ui_lambda_x 0.175 0.165 0.140 Latent field
11 ui_lambda_x 0.121 0.108 0.111 Latent field
12 ui_lambda_x 0.110 0.088 0.109 Latent field
13 ui_lambda_x 0.117 0.118 0.133 Latent field
14 ui_lambda_x 0.114 0.104 0.112 Latent field
15 ui_lambda_x 0.103 0.137 0.131 Latent field
16 ui_lambda_x 0.114 0.097 0.104 Latent field
17 ui_lambda_x 0.124 0.103 0.110 Latent field
18 ui_lambda_x 0.105 0.101 0.099 Latent field
19 ui_lambda_x 0.093 0.135 0.110 Latent field
20 ui_lambda_x 0.122 0.113 0.099 Latent field
21 ui_lambda_x 0.120 0.112 0.110 Latent field
22 ui_lambda_x 0.098 0.104 0.091 Latent field
23 ui_lambda_x 0.117 0.105 0.105 Latent field
24 ui_lambda_x 0.104 0.126 0.091 Latent field
25 ui_lambda_x 0.125 0.108 0.125 Latent field
26 ui_lambda_x 0.143 0.126 0.125 Latent field
27 ui_lambda_x 0.122 0.101 0.107 Latent field
28 ui_lambda_x 0.087 0.093 0.107 Latent field
29 ui_lambda_x 0.079 0.112 0.104 Latent field
30 ui_lambda_x 0.116 0.117 0.132 Latent field
31 ui_lambda_x 0.123 0.122 0.122 Latent field
32 ui_lambda_x 0.127 0.099 0.140 Latent field
1 ui_anc_rho_x 0.046 0.077 0.070 Latent field
2 ui_anc_rho_x 0.030 0.080 0.032 Latent field
3 ui_anc_rho_x 0.059 0.056 0.032 Latent field
4 ui_anc_rho_x 0.050 0.089 0.063 Latent field
5 ui_anc_rho_x 0.059 0.059 0.048 Latent field
6 ui_anc_rho_x 0.082 0.030 0.034 Latent field
7 ui_anc_rho_x 0.029 0.051 0.051 Latent field
8 ui_anc_rho_x 0.017 0.049 0.041 Latent field
9 ui_anc_rho_x 0.047 0.040 0.025 Latent field
10 ui_anc_rho_x 0.027 0.115 0.093 Latent field
11 ui_anc_rho_x 0.025 0.054 0.066 Latent field
12 ui_anc_rho_x 0.108 0.035 0.053 Latent field
13 ui_anc_rho_x 0.025 0.024 0.025 Latent field
14 ui_anc_rho_x 0.043 0.067 0.070 Latent field
15 ui_anc_rho_x 0.045 0.084 0.068 Latent field
16 ui_anc_rho_x 0.062 0.027 0.015 Latent field
17 ui_anc_rho_x 0.078 0.041 0.024 Latent field
18 ui_anc_rho_x 0.045 0.043 0.085 Latent field
19 ui_anc_rho_x 0.024 0.054 0.040 Latent field
20 ui_anc_rho_x 0.046 0.047 0.061 Latent field
21 ui_anc_rho_x 0.046 0.075 0.052 Latent field
22 ui_anc_rho_x 0.106 0.082 0.038 Latent field
23 ui_anc_rho_x 0.033 0.066 0.071 Latent field
24 ui_anc_rho_x 0.055 0.097 0.092 Latent field
25 ui_anc_rho_x 0.037 0.085 0.063 Latent field
26 ui_anc_rho_x 0.030 0.066 0.094 Latent field
27 ui_anc_rho_x 0.077 0.112 0.070 Latent field
28 ui_anc_rho_x 0.026 0.032 0.046 Latent field
29 ui_anc_rho_x 0.116 0.048 0.062 Latent field
30 ui_anc_rho_x 0.035 0.028 0.018 Latent field
31 ui_anc_rho_x 0.027 0.036 0.077 Latent field
32 ui_anc_rho_x 0.025 0.051 0.039 Latent field
1 ui_anc_alpha_x 0.074 0.064 0.068 Latent field
2 ui_anc_alpha_x 0.083 0.062 0.057 Latent field
3 ui_anc_alpha_x 0.115 0.137 0.100 Latent field
4 ui_anc_alpha_x 0.074 0.063 0.037 Latent field
5 ui_anc_alpha_x 0.036 0.071 0.055 Latent field
6 ui_anc_alpha_x 0.038 0.054 0.037 Latent field
7 ui_anc_alpha_x 0.079 0.069 0.071 Latent field
8 ui_anc_alpha_x 0.051 0.057 0.058 Latent field
9 ui_anc_alpha_x 0.091 0.071 0.090 Latent field
10 ui_anc_alpha_x 0.049 0.039 0.067 Latent field
11 ui_anc_alpha_x 0.050 0.039 0.040 Latent field
12 ui_anc_alpha_x 0.044 0.076 0.091 Latent field
13 ui_anc_alpha_x 0.042 0.063 0.044 Latent field
14 ui_anc_alpha_x 0.077 0.086 0.111 Latent field
15 ui_anc_alpha_x 0.110 0.077 0.115 Latent field
16 ui_anc_alpha_x 0.106 0.124 0.090 Latent field
17 ui_anc_alpha_x 0.084 0.100 0.105 Latent field
18 ui_anc_alpha_x 0.158 0.175 0.148 Latent field
19 ui_anc_alpha_x 0.068 0.107 0.074 Latent field
20 ui_anc_alpha_x 0.077 0.051 0.050 Latent field
21 ui_anc_alpha_x 0.086 0.064 0.086 Latent field
22 ui_anc_alpha_x 0.069 0.047 0.058 Latent field
23 ui_anc_alpha_x 0.044 0.053 0.070 Latent field
24 ui_anc_alpha_x 0.055 0.036 0.067 Latent field
25 ui_anc_alpha_x 0.098 0.086 0.069 Latent field
26 ui_anc_alpha_x 0.069 0.041 0.077 Latent field
27 ui_anc_alpha_x 0.044 0.071 0.069 Latent field
28 ui_anc_alpha_x 0.077 0.060 0.064 Latent field
29 ui_anc_alpha_x 0.148 0.168 0.169 Latent field
30 ui_anc_alpha_x 0.058 0.046 0.046 Latent field
31 ui_anc_alpha_x 0.049 0.046 0.060 Latent field
32 ui_anc_alpha_x 0.066 0.087 0.050 Latent field
1 log_or_gamma 0.028 0.103 0.132 Latent field
2 log_or_gamma 0.037 0.081 0.067 Latent field
3 log_or_gamma 0.051 0.026 0.030 Latent field
4 log_or_gamma 0.029 0.050 0.059 Latent field
5 log_or_gamma 0.030 0.097 0.078 Latent field
6 log_or_gamma 0.031 0.051 0.056 Latent field
7 log_or_gamma 0.026 0.023 0.029 Latent field
8 log_or_gamma 0.046 0.024 0.037 Latent field
9 log_or_gamma 0.039 0.086 0.062 Latent field
10 log_or_gamma 0.021 0.044 0.033 Latent field
11 log_or_gamma 0.043 0.017 0.025 Latent field
12 log_or_gamma 0.050 0.117 0.106 Latent field
13 log_or_gamma 0.029 0.062 0.044 Latent field
14 log_or_gamma 0.050 0.028 0.021 Latent field
15 log_or_gamma 0.035 0.042 0.060 Latent field
16 log_or_gamma 0.029 0.050 0.046 Latent field
17 log_or_gamma 0.022 0.060 0.041 Latent field
18 log_or_gamma 0.027 0.128 0.100 Latent field
19 log_or_gamma 0.028 0.045 0.054 Latent field
20 log_or_gamma 0.032 0.031 0.033 Latent field
21 log_or_gamma 0.050 0.042 0.044 Latent field
22 log_or_gamma 0.034 0.025 0.036 Latent field
23 log_or_gamma 0.037 0.049 0.044 Latent field
24 log_or_gamma 0.024 0.054 0.075 Latent field
25 log_or_gamma 0.021 0.069 0.061 Latent field
26 log_or_gamma 0.045 0.043 0.029 Latent field
27 log_or_gamma 0.034 0.020 0.029 Latent field
28 log_or_gamma 0.034 0.020 0.025 Latent field
29 log_or_gamma 0.041 0.042 0.033 Latent field
30 log_or_gamma 0.030 0.059 0.031 Latent field
31 log_or_gamma 0.039 0.069 0.075 Latent field
32 log_or_gamma 0.025 0.040 0.043 Latent field

3.2.2 Hyperparameters

ks_table(ks_summary, type = "Latent field")
index Parameter KS(adam, tmbstan) KS(aghq, tmbstan) KS(TMB, tmbstan) Type
1 beta_rho 0.073 0.080 0.071 Latent field
2 beta_rho 0.074 0.065 0.066 Latent field
1 beta_alpha 0.069 0.040 0.079 Latent field
2 beta_alpha 0.111 0.111 0.115 Latent field
1 beta_lambda 0.031 0.095 0.128 Latent field
2 beta_lambda 0.023 0.046 0.026 Latent field
1 beta_anc_rho 0.032 0.113 0.138 Latent field
1 beta_anc_alpha 0.084 0.077 0.093 Latent field
1 u_rho_x 0.050 0.055 0.051 Latent field
2 u_rho_x 0.041 0.105 0.060 Latent field
3 u_rho_x 0.031 0.020 0.034 Latent field
4 u_rho_x 0.037 0.090 0.065 Latent field
5 u_rho_x 0.125 0.062 0.115 Latent field
6 u_rho_x 0.125 0.152 0.136 Latent field
7 u_rho_x 0.084 0.157 0.157 Latent field
8 u_rho_x 0.059 0.041 0.030 Latent field
9 u_rho_x 0.042 0.067 0.030 Latent field
10 u_rho_x 0.052 0.082 0.084 Latent field
11 u_rho_x 0.062 0.045 0.042 Latent field
12 u_rho_x 0.116 0.149 0.164 Latent field
13 u_rho_x 0.038 0.050 0.056 Latent field
14 u_rho_x 0.094 0.086 0.104 Latent field
15 u_rho_x 0.058 0.019 0.038 Latent field
16 u_rho_x 0.045 0.031 0.035 Latent field
17 u_rho_x 0.020 0.031 0.060 Latent field
18 u_rho_x 0.063 0.031 0.045 Latent field
19 u_rho_x 0.097 0.044 0.065 Latent field
20 u_rho_x 0.038 0.023 0.032 Latent field
21 u_rho_x 0.045 0.096 0.081 Latent field
22 u_rho_x 0.164 0.131 0.149 Latent field
23 u_rho_x 0.057 0.038 0.039 Latent field
24 u_rho_x 0.105 0.036 0.046 Latent field
25 u_rho_x 0.045 0.062 0.048 Latent field
26 u_rho_x 0.065 0.033 0.055 Latent field
27 u_rho_x 0.099 0.099 0.070 Latent field
28 u_rho_x 0.030 0.034 0.024 Latent field
29 u_rho_x 0.072 0.087 0.116 Latent field
30 u_rho_x 0.070 0.042 0.045 Latent field
31 u_rho_x 0.067 0.048 0.066 Latent field
32 u_rho_x 0.035 0.092 0.083 Latent field
1 us_rho_x 0.134 0.170 0.174 Latent field
2 us_rho_x 0.135 0.107 0.130 Latent field
3 us_rho_x 0.106 0.084 0.110 Latent field
4 us_rho_x 0.105 0.082 0.072 Latent field
5 us_rho_x 0.079 0.067 0.058 Latent field
6 us_rho_x 0.203 0.194 0.180 Latent field
7 us_rho_x 0.057 0.061 0.033 Latent field
8 us_rho_x 0.075 0.068 0.087 Latent field
9 us_rho_x 0.070 0.055 0.035 Latent field
10 us_rho_x 0.062 0.073 0.051 Latent field
11 us_rho_x 0.088 0.085 0.074 Latent field
12 us_rho_x 0.109 0.087 0.111 Latent field
13 us_rho_x 0.073 0.054 0.062 Latent field
14 us_rho_x 0.057 0.085 0.042 Latent field
15 us_rho_x 0.057 0.070 0.067 Latent field
16 us_rho_x 0.062 0.081 0.113 Latent field
17 us_rho_x 0.040 0.058 0.089 Latent field
18 us_rho_x 0.110 0.114 0.114 Latent field
19 us_rho_x 0.062 0.127 0.032 Latent field
20 us_rho_x 0.106 0.138 0.116 Latent field
21 us_rho_x 0.096 0.085 0.095 Latent field
22 us_rho_x 0.114 0.075 0.099 Latent field
23 us_rho_x 0.092 0.072 0.054 Latent field
24 us_rho_x 0.035 0.037 0.068 Latent field
25 us_rho_x 0.062 0.098 0.074 Latent field
26 us_rho_x 0.079 0.080 0.103 Latent field
27 us_rho_x 0.052 0.031 0.033 Latent field
28 us_rho_x 0.059 0.043 0.052 Latent field
29 us_rho_x 0.072 0.108 0.087 Latent field
30 us_rho_x 0.084 0.066 0.070 Latent field
31 us_rho_x 0.051 0.058 0.043 Latent field
32 us_rho_x 0.109 0.040 0.066 Latent field
1 u_rho_xs 0.128 0.080 0.078 Latent field
2 u_rho_xs 0.087 0.111 0.094 Latent field
3 u_rho_xs 0.112 0.123 0.120 Latent field
4 u_rho_xs 0.119 0.104 0.121 Latent field
5 u_rho_xs 0.193 0.163 0.203 Latent field
6 u_rho_xs 0.268 0.227 0.266 Latent field
7 u_rho_xs 0.190 0.200 0.202 Latent field
8 u_rho_xs 0.107 0.107 0.106 Latent field
9 u_rho_xs 0.123 0.139 0.124 Latent field
10 u_rho_xs 0.084 0.078 0.097 Latent field
11 u_rho_xs 0.105 0.098 0.099 Latent field
12 u_rho_xs 0.246 0.204 0.241 Latent field
13 u_rho_xs 0.104 0.135 0.146 Latent field
14 u_rho_xs 0.138 0.136 0.171 Latent field
15 u_rho_xs 0.159 0.151 0.176 Latent field
16 u_rho_xs 0.103 0.104 0.123 Latent field
17 u_rho_xs 0.102 0.095 0.118 Latent field
18 u_rho_xs 0.187 0.145 0.191 Latent field
19 u_rho_xs 0.172 0.150 0.193 Latent field
20 u_rho_xs 0.130 0.101 0.117 Latent field
21 u_rho_xs 0.110 0.127 0.137 Latent field
22 u_rho_xs 0.262 0.234 0.268 Latent field
23 u_rho_xs 0.165 0.167 0.163 Latent field
24 u_rho_xs 0.211 0.185 0.196 Latent field
25 u_rho_xs 0.115 0.100 0.115 Latent field
26 u_rho_xs 0.146 0.146 0.135 Latent field
27 u_rho_xs 0.205 0.177 0.215 Latent field
28 u_rho_xs 0.139 0.118 0.110 Latent field
29 u_rho_xs 0.203 0.173 0.203 Latent field
30 u_rho_xs 0.144 0.120 0.117 Latent field
31 u_rho_xs 0.155 0.135 0.163 Latent field
32 u_rho_xs 0.135 0.124 0.093 Latent field
1 us_rho_xs 0.036 0.036 0.029 Latent field
2 us_rho_xs 0.023 0.024 0.039 Latent field
3 us_rho_xs 0.027 0.031 0.046 Latent field
4 us_rho_xs 0.016 0.035 0.023 Latent field
5 us_rho_xs 0.044 0.045 0.051 Latent field
6 us_rho_xs 0.034 0.056 0.021 Latent field
7 us_rho_xs 0.077 0.060 0.050 Latent field
8 us_rho_xs 0.035 0.049 0.026 Latent field
9 us_rho_xs 0.028 0.039 0.037 Latent field
10 us_rho_xs 0.051 0.024 0.021 Latent field
11 us_rho_xs 0.026 0.037 0.057 Latent field
12 us_rho_xs 0.052 0.050 0.037 Latent field
13 us_rho_xs 0.040 0.039 0.031 Latent field
14 us_rho_xs 0.022 0.028 0.033 Latent field
15 us_rho_xs 0.032 0.056 0.034 Latent field
16 us_rho_xs 0.021 0.050 0.020 Latent field
17 us_rho_xs 0.027 0.025 0.021 Latent field
18 us_rho_xs 0.030 0.037 0.032 Latent field
19 us_rho_xs 0.041 0.044 0.023 Latent field
20 us_rho_xs 0.030 0.044 0.036 Latent field
21 us_rho_xs 0.041 0.027 0.024 Latent field
22 us_rho_xs 0.040 0.039 0.025 Latent field
23 us_rho_xs 0.045 0.042 0.023 Latent field
24 us_rho_xs 0.038 0.038 0.035 Latent field
25 us_rho_xs 0.076 0.049 0.051 Latent field
26 us_rho_xs 0.043 0.040 0.036 Latent field
27 us_rho_xs 0.047 0.022 0.049 Latent field
28 us_rho_xs 0.041 0.036 0.025 Latent field
29 us_rho_xs 0.031 0.051 0.020 Latent field
30 us_rho_xs 0.053 0.032 0.037 Latent field
31 us_rho_xs 0.042 0.045 0.058 Latent field
32 us_rho_xs 0.031 0.031 0.028 Latent field
1 u_rho_a 0.075 0.077 0.072 Latent field
2 u_rho_a 0.074 0.084 0.076 Latent field
3 u_rho_a 0.069 0.084 0.075 Latent field
4 u_rho_a 0.081 0.082 0.072 Latent field
5 u_rho_a 0.069 0.084 0.070 Latent field
6 u_rho_a 0.086 0.082 0.070 Latent field
7 u_rho_a 0.070 0.090 0.072 Latent field
8 u_rho_a 0.073 0.080 0.077 Latent field
9 u_rho_a 0.081 0.078 0.070 Latent field
10 u_rho_a 0.080 0.087 0.070 Latent field
1 u_rho_as 0.072 0.041 0.067 Latent field
2 u_rho_as 0.072 0.063 0.066 Latent field
3 u_rho_as 0.072 0.059 0.065 Latent field
4 u_rho_as 0.078 0.064 0.067 Latent field
5 u_rho_as 0.065 0.061 0.070 Latent field
6 u_rho_as 0.069 0.060 0.066 Latent field
7 u_rho_as 0.071 0.056 0.065 Latent field
8 u_rho_as 0.060 0.061 0.064 Latent field
9 u_rho_as 0.072 0.080 0.065 Latent field
10 u_rho_as 0.078 0.085 0.071 Latent field
1 u_alpha_x 0.122 0.120 0.157 Latent field
2 u_alpha_x 0.126 0.111 0.158 Latent field
3 u_alpha_x 0.114 0.095 0.140 Latent field
4 u_alpha_x 0.142 0.137 0.131 Latent field
5 u_alpha_x 0.139 0.109 0.124 Latent field
6 u_alpha_x 0.104 0.083 0.076 Latent field
7 u_alpha_x 0.107 0.059 0.058 Latent field
8 u_alpha_x 0.177 0.135 0.157 Latent field
9 u_alpha_x 0.161 0.129 0.179 Latent field
10 u_alpha_x 0.185 0.132 0.169 Latent field
11 u_alpha_x 0.154 0.113 0.154 Latent field
12 u_alpha_x 0.116 0.056 0.072 Latent field
13 u_alpha_x 0.158 0.093 0.146 Latent field
14 u_alpha_x 0.087 0.047 0.102 Latent field
15 u_alpha_x 0.099 0.073 0.112 Latent field
16 u_alpha_x 0.059 0.058 0.047 Latent field
17 u_alpha_x 0.090 0.092 0.130 Latent field
18 u_alpha_x 0.123 0.140 0.134 Latent field
19 u_alpha_x 0.112 0.117 0.124 Latent field
20 u_alpha_x 0.118 0.109 0.096 Latent field
21 u_alpha_x 0.171 0.148 0.173 Latent field
22 u_alpha_x 0.119 0.116 0.159 Latent field
23 u_alpha_x 0.134 0.119 0.123 Latent field
24 u_alpha_x 0.133 0.081 0.134 Latent field
25 u_alpha_x 0.099 0.089 0.130 Latent field
26 u_alpha_x 0.117 0.071 0.133 Latent field
27 u_alpha_x 0.131 0.132 0.148 Latent field
28 u_alpha_x 0.091 0.078 0.112 Latent field
29 u_alpha_x 0.098 0.097 0.096 Latent field
30 u_alpha_x 0.109 0.087 0.141 Latent field
31 u_alpha_x 0.086 0.052 0.102 Latent field
32 u_alpha_x 0.069 0.061 0.064 Latent field
1 us_alpha_x 0.069 0.076 0.095 Latent field
2 us_alpha_x 0.070 0.062 0.079 Latent field
3 us_alpha_x 0.085 0.066 0.095 Latent field
4 us_alpha_x 0.066 0.068 0.079 Latent field
5 us_alpha_x 0.107 0.067 0.099 Latent field
6 us_alpha_x 0.094 0.063 0.089 Latent field
7 us_alpha_x 0.025 0.026 0.027 Latent field
8 us_alpha_x 0.144 0.070 0.110 Latent field
9 us_alpha_x 0.135 0.075 0.122 Latent field
10 us_alpha_x 0.131 0.067 0.104 Latent field
11 us_alpha_x 0.103 0.057 0.099 Latent field
12 us_alpha_x 0.098 0.048 0.067 Latent field
13 us_alpha_x 0.103 0.061 0.098 Latent field
14 us_alpha_x 0.064 0.051 0.072 Latent field
15 us_alpha_x 0.087 0.050 0.093 Latent field
16 us_alpha_x 0.043 0.035 0.022 Latent field
17 us_alpha_x 0.092 0.065 0.092 Latent field
18 us_alpha_x 0.084 0.076 0.074 Latent field
19 us_alpha_x 0.084 0.073 0.095 Latent field
20 us_alpha_x 0.083 0.074 0.087 Latent field
21 us_alpha_x 0.131 0.083 0.100 Latent field
22 us_alpha_x 0.184 0.106 0.169 Latent field
23 us_alpha_x 0.084 0.077 0.109 Latent field
24 us_alpha_x 0.103 0.064 0.116 Latent field
25 us_alpha_x 0.102 0.061 0.104 Latent field
26 us_alpha_x 0.074 0.061 0.089 Latent field
27 us_alpha_x 0.077 0.057 0.092 Latent field
28 us_alpha_x 0.066 0.047 0.072 Latent field
29 us_alpha_x 0.106 0.086 0.122 Latent field
30 us_alpha_x 0.072 0.040 0.091 Latent field
31 us_alpha_x 0.051 0.035 0.076 Latent field
32 us_alpha_x 0.041 0.030 0.057 Latent field
1 u_alpha_xs 0.034 0.069 0.054 Latent field
2 u_alpha_xs 0.069 0.066 0.071 Latent field
3 u_alpha_xs 0.034 0.073 0.057 Latent field
4 u_alpha_xs 0.132 0.138 0.109 Latent field
5 u_alpha_xs 0.128 0.050 0.077 Latent field
6 u_alpha_xs 0.033 0.043 0.028 Latent field
7 u_alpha_xs 0.051 0.057 0.073 Latent field
8 u_alpha_xs 0.068 0.067 0.079 Latent field
9 u_alpha_xs 0.085 0.059 0.073 Latent field
10 u_alpha_xs 0.096 0.084 0.143 Latent field
11 u_alpha_xs 0.129 0.080 0.116 Latent field
12 u_alpha_xs 0.107 0.094 0.127 Latent field
13 u_alpha_xs 0.104 0.043 0.106 Latent field
14 u_alpha_xs 0.049 0.076 0.054 Latent field
15 u_alpha_xs 0.106 0.103 0.166 Latent field
16 u_alpha_xs 0.123 0.103 0.136 Latent field
17 u_alpha_xs 0.085 0.063 0.060 Latent field
18 u_alpha_xs 0.148 0.161 0.142 Latent field
19 u_alpha_xs 0.059 0.053 0.049 Latent field
20 u_alpha_xs 0.047 0.051 0.062 Latent field
21 u_alpha_xs 0.086 0.079 0.081 Latent field
22 u_alpha_xs 0.166 0.120 0.131 Latent field
23 u_alpha_xs 0.089 0.070 0.097 Latent field
24 u_alpha_xs 0.133 0.100 0.125 Latent field
25 u_alpha_xs 0.155 0.101 0.101 Latent field
26 u_alpha_xs 0.064 0.052 0.059 Latent field
27 u_alpha_xs 0.119 0.126 0.130 Latent field
28 u_alpha_xs 0.083 0.036 0.042 Latent field
29 u_alpha_xs 0.173 0.121 0.162 Latent field
30 u_alpha_xs 0.095 0.078 0.109 Latent field
31 u_alpha_xs 0.117 0.054 0.113 Latent field
32 u_alpha_xs 0.119 0.065 0.116 Latent field
1 us_alpha_xs 0.042 0.038 0.058 Latent field
2 us_alpha_xs 0.032 0.068 0.048 Latent field
3 us_alpha_xs 0.049 0.034 0.042 Latent field
4 us_alpha_xs 0.058 0.070 0.079 Latent field
5 us_alpha_xs 0.070 0.070 0.060 Latent field
6 us_alpha_xs 0.061 0.071 0.064 Latent field
7 us_alpha_xs 0.034 0.032 0.025 Latent field
8 us_alpha_xs 0.093 0.057 0.103 Latent field
9 us_alpha_xs 0.100 0.065 0.110 Latent field
10 us_alpha_xs 0.114 0.070 0.120 Latent field
11 us_alpha_xs 0.101 0.091 0.123 Latent field
12 us_alpha_xs 0.098 0.089 0.124 Latent field
13 us_alpha_xs 0.116 0.053 0.089 Latent field
14 us_alpha_xs 0.069 0.033 0.072 Latent field
15 us_alpha_xs 0.110 0.091 0.140 Latent field
16 us_alpha_xs 0.142 0.061 0.116 Latent field
17 us_alpha_xs 0.082 0.024 0.073 Latent field
18 us_alpha_xs 0.111 0.027 0.099 Latent field
19 us_alpha_xs 0.037 0.056 0.025 Latent field
20 us_alpha_xs 0.034 0.045 0.035 Latent field
21 us_alpha_xs 0.070 0.026 0.072 Latent field
22 us_alpha_xs 0.096 0.090 0.102 Latent field
23 us_alpha_xs 0.125 0.064 0.123 Latent field
24 us_alpha_xs 0.150 0.082 0.124 Latent field
25 us_alpha_xs 0.084 0.070 0.078 Latent field
26 us_alpha_xs 0.155 0.084 0.132 Latent field
27 us_alpha_xs 0.141 0.079 0.129 Latent field
28 us_alpha_xs 0.115 0.073 0.095 Latent field
29 us_alpha_xs 0.137 0.079 0.138 Latent field
30 us_alpha_xs 0.166 0.085 0.154 Latent field
31 us_alpha_xs 0.130 0.072 0.122 Latent field
32 us_alpha_xs 0.140 0.070 0.123 Latent field
1 u_alpha_a 0.055 0.033 0.070 Latent field
2 u_alpha_a 0.069 0.036 0.078 Latent field
3 u_alpha_a 0.066 0.031 0.070 Latent field
4 u_alpha_a 0.052 0.035 0.074 Latent field
5 u_alpha_a 0.073 0.037 0.078 Latent field
6 u_alpha_a 0.060 0.025 0.072 Latent field
7 u_alpha_a 0.069 0.023 0.076 Latent field
8 u_alpha_a 0.068 0.030 0.073 Latent field
9 u_alpha_a 0.065 0.042 0.073 Latent field
10 u_alpha_a 0.064 0.036 0.068 Latent field
11 u_alpha_a 0.075 0.034 0.070 Latent field
12 u_alpha_a 0.067 0.044 0.075 Latent field
13 u_alpha_a 0.066 0.042 0.068 Latent field
1 u_alpha_as 0.067 0.094 0.081 Latent field
2 u_alpha_as 0.100 0.103 0.106 Latent field
3 u_alpha_as 0.120 0.104 0.131 Latent field
4 u_alpha_as 0.129 0.104 0.107 Latent field
5 u_alpha_as 0.155 0.103 0.119 Latent field
6 u_alpha_as 0.094 0.074 0.095 Latent field
7 u_alpha_as 0.077 0.067 0.077 Latent field
8 u_alpha_as 0.060 0.057 0.060 Latent field
9 u_alpha_as 0.059 0.040 0.058 Latent field
10 u_alpha_as 0.064 0.044 0.063 Latent field
1 u_alpha_xa 0.033 0.056 0.051 Latent field
2 u_alpha_xa 0.067 0.039 0.040 Latent field
3 u_alpha_xa 0.058 0.036 0.039 Latent field
4 u_alpha_xa 0.080 0.063 0.072 Latent field
5 u_alpha_xa 0.109 0.074 0.103 Latent field
6 u_alpha_xa 0.109 0.122 0.100 Latent field
7 u_alpha_xa 0.081 0.088 0.090 Latent field
8 u_alpha_xa 0.061 0.048 0.081 Latent field
9 u_alpha_xa 0.069 0.037 0.053 Latent field
10 u_alpha_xa 0.103 0.092 0.161 Latent field
11 u_alpha_xa 0.094 0.086 0.122 Latent field
12 u_alpha_xa 0.116 0.068 0.121 Latent field
13 u_alpha_xa 0.073 0.017 0.083 Latent field
14 u_alpha_xa 0.084 0.094 0.095 Latent field
15 u_alpha_xa 0.054 0.043 0.062 Latent field
16 u_alpha_xa 0.038 0.052 0.048 Latent field
17 u_alpha_xa 0.046 0.032 0.026 Latent field
18 u_alpha_xa 0.038 0.037 0.033 Latent field
19 u_alpha_xa 0.098 0.053 0.090 Latent field
20 u_alpha_xa 0.042 0.039 0.054 Latent field
21 u_alpha_xa 0.082 0.077 0.105 Latent field
22 u_alpha_xa 0.218 0.184 0.220 Latent field
23 u_alpha_xa 0.024 0.037 0.051 Latent field
24 u_alpha_xa 0.061 0.020 0.055 Latent field
25 u_alpha_xa 0.091 0.063 0.057 Latent field
26 u_alpha_xa 0.033 0.053 0.020 Latent field
27 u_alpha_xa 0.097 0.122 0.104 Latent field
28 u_alpha_xa 0.069 0.045 0.046 Latent field
29 u_alpha_xa 0.035 0.050 0.053 Latent field
30 u_alpha_xa 0.058 0.062 0.060 Latent field
31 u_alpha_xa 0.026 0.035 0.044 Latent field
32 u_alpha_xa 0.038 0.027 0.054 Latent field
1 ui_lambda_x 0.112 0.124 0.119 Latent field
2 ui_lambda_x 0.123 0.121 0.126 Latent field
3 ui_lambda_x 0.101 0.126 0.108 Latent field
4 ui_lambda_x 0.108 0.121 0.129 Latent field
5 ui_lambda_x 0.124 0.101 0.114 Latent field
6 ui_lambda_x 0.093 0.092 0.087 Latent field
7 ui_lambda_x 0.114 0.136 0.109 Latent field
8 ui_lambda_x 0.115 0.119 0.102 Latent field
9 ui_lambda_x 0.117 0.097 0.105 Latent field
10 ui_lambda_x 0.175 0.165 0.140 Latent field
11 ui_lambda_x 0.121 0.108 0.111 Latent field
12 ui_lambda_x 0.110 0.088 0.109 Latent field
13 ui_lambda_x 0.117 0.118 0.133 Latent field
14 ui_lambda_x 0.114 0.104 0.112 Latent field
15 ui_lambda_x 0.103 0.137 0.131 Latent field
16 ui_lambda_x 0.114 0.097 0.104 Latent field
17 ui_lambda_x 0.124 0.103 0.110 Latent field
18 ui_lambda_x 0.105 0.101 0.099 Latent field
19 ui_lambda_x 0.093 0.135 0.110 Latent field
20 ui_lambda_x 0.122 0.113 0.099 Latent field
21 ui_lambda_x 0.120 0.112 0.110 Latent field
22 ui_lambda_x 0.098 0.104 0.091 Latent field
23 ui_lambda_x 0.117 0.105 0.105 Latent field
24 ui_lambda_x 0.104 0.126 0.091 Latent field
25 ui_lambda_x 0.125 0.108 0.125 Latent field
26 ui_lambda_x 0.143 0.126 0.125 Latent field
27 ui_lambda_x 0.122 0.101 0.107 Latent field
28 ui_lambda_x 0.087 0.093 0.107 Latent field
29 ui_lambda_x 0.079 0.112 0.104 Latent field
30 ui_lambda_x 0.116 0.117 0.132 Latent field
31 ui_lambda_x 0.123 0.122 0.122 Latent field
32 ui_lambda_x 0.127 0.099 0.140 Latent field
1 ui_anc_rho_x 0.046 0.077 0.070 Latent field
2 ui_anc_rho_x 0.030 0.080 0.032 Latent field
3 ui_anc_rho_x 0.059 0.056 0.032 Latent field
4 ui_anc_rho_x 0.050 0.089 0.063 Latent field
5 ui_anc_rho_x 0.059 0.059 0.048 Latent field
6 ui_anc_rho_x 0.082 0.030 0.034 Latent field
7 ui_anc_rho_x 0.029 0.051 0.051 Latent field
8 ui_anc_rho_x 0.017 0.049 0.041 Latent field
9 ui_anc_rho_x 0.047 0.040 0.025 Latent field
10 ui_anc_rho_x 0.027 0.115 0.093 Latent field
11 ui_anc_rho_x 0.025 0.054 0.066 Latent field
12 ui_anc_rho_x 0.108 0.035 0.053 Latent field
13 ui_anc_rho_x 0.025 0.024 0.025 Latent field
14 ui_anc_rho_x 0.043 0.067 0.070 Latent field
15 ui_anc_rho_x 0.045 0.084 0.068 Latent field
16 ui_anc_rho_x 0.062 0.027 0.015 Latent field
17 ui_anc_rho_x 0.078 0.041 0.024 Latent field
18 ui_anc_rho_x 0.045 0.043 0.085 Latent field
19 ui_anc_rho_x 0.024 0.054 0.040 Latent field
20 ui_anc_rho_x 0.046 0.047 0.061 Latent field
21 ui_anc_rho_x 0.046 0.075 0.052 Latent field
22 ui_anc_rho_x 0.106 0.082 0.038 Latent field
23 ui_anc_rho_x 0.033 0.066 0.071 Latent field
24 ui_anc_rho_x 0.055 0.097 0.092 Latent field
25 ui_anc_rho_x 0.037 0.085 0.063 Latent field
26 ui_anc_rho_x 0.030 0.066 0.094 Latent field
27 ui_anc_rho_x 0.077 0.112 0.070 Latent field
28 ui_anc_rho_x 0.026 0.032 0.046 Latent field
29 ui_anc_rho_x 0.116 0.048 0.062 Latent field
30 ui_anc_rho_x 0.035 0.028 0.018 Latent field
31 ui_anc_rho_x 0.027 0.036 0.077 Latent field
32 ui_anc_rho_x 0.025 0.051 0.039 Latent field
1 ui_anc_alpha_x 0.074 0.064 0.068 Latent field
2 ui_anc_alpha_x 0.083 0.062 0.057 Latent field
3 ui_anc_alpha_x 0.115 0.137 0.100 Latent field
4 ui_anc_alpha_x 0.074 0.063 0.037 Latent field
5 ui_anc_alpha_x 0.036 0.071 0.055 Latent field
6 ui_anc_alpha_x 0.038 0.054 0.037 Latent field
7 ui_anc_alpha_x 0.079 0.069 0.071 Latent field
8 ui_anc_alpha_x 0.051 0.057 0.058 Latent field
9 ui_anc_alpha_x 0.091 0.071 0.090 Latent field
10 ui_anc_alpha_x 0.049 0.039 0.067 Latent field
11 ui_anc_alpha_x 0.050 0.039 0.040 Latent field
12 ui_anc_alpha_x 0.044 0.076 0.091 Latent field
13 ui_anc_alpha_x 0.042 0.063 0.044 Latent field
14 ui_anc_alpha_x 0.077 0.086 0.111 Latent field
15 ui_anc_alpha_x 0.110 0.077 0.115 Latent field
16 ui_anc_alpha_x 0.106 0.124 0.090 Latent field
17 ui_anc_alpha_x 0.084 0.100 0.105 Latent field
18 ui_anc_alpha_x 0.158 0.175 0.148 Latent field
19 ui_anc_alpha_x 0.068 0.107 0.074 Latent field
20 ui_anc_alpha_x 0.077 0.051 0.050 Latent field
21 ui_anc_alpha_x 0.086 0.064 0.086 Latent field
22 ui_anc_alpha_x 0.069 0.047 0.058 Latent field
23 ui_anc_alpha_x 0.044 0.053 0.070 Latent field
24 ui_anc_alpha_x 0.055 0.036 0.067 Latent field
25 ui_anc_alpha_x 0.098 0.086 0.069 Latent field
26 ui_anc_alpha_x 0.069 0.041 0.077 Latent field
27 ui_anc_alpha_x 0.044 0.071 0.069 Latent field
28 ui_anc_alpha_x 0.077 0.060 0.064 Latent field
29 ui_anc_alpha_x 0.148 0.168 0.169 Latent field
30 ui_anc_alpha_x 0.058 0.046 0.046 Latent field
31 ui_anc_alpha_x 0.049 0.046 0.060 Latent field
32 ui_anc_alpha_x 0.066 0.087 0.050 Latent field
1 log_or_gamma 0.028 0.103 0.132 Latent field
2 log_or_gamma 0.037 0.081 0.067 Latent field
3 log_or_gamma 0.051 0.026 0.030 Latent field
4 log_or_gamma 0.029 0.050 0.059 Latent field
5 log_or_gamma 0.030 0.097 0.078 Latent field
6 log_or_gamma 0.031 0.051 0.056 Latent field
7 log_or_gamma 0.026 0.023 0.029 Latent field
8 log_or_gamma 0.046 0.024 0.037 Latent field
9 log_or_gamma 0.039 0.086 0.062 Latent field
10 log_or_gamma 0.021 0.044 0.033 Latent field
11 log_or_gamma 0.043 0.017 0.025 Latent field
12 log_or_gamma 0.050 0.117 0.106 Latent field
13 log_or_gamma 0.029 0.062 0.044 Latent field
14 log_or_gamma 0.050 0.028 0.021 Latent field
15 log_or_gamma 0.035 0.042 0.060 Latent field
16 log_or_gamma 0.029 0.050 0.046 Latent field
17 log_or_gamma 0.022 0.060 0.041 Latent field
18 log_or_gamma 0.027 0.128 0.100 Latent field
19 log_or_gamma 0.028 0.045 0.054 Latent field
20 log_or_gamma 0.032 0.031 0.033 Latent field
21 log_or_gamma 0.050 0.042 0.044 Latent field
22 log_or_gamma 0.034 0.025 0.036 Latent field
23 log_or_gamma 0.037 0.049 0.044 Latent field
24 log_or_gamma 0.024 0.054 0.075 Latent field
25 log_or_gamma 0.021 0.069 0.061 Latent field
26 log_or_gamma 0.045 0.043 0.029 Latent field
27 log_or_gamma 0.034 0.020 0.029 Latent field
28 log_or_gamma 0.034 0.020 0.025 Latent field
29 log_or_gamma 0.041 0.042 0.033 Latent field
30 log_or_gamma 0.030 0.059 0.031 Latent field
31 log_or_gamma 0.039 0.069 0.075 Latent field
32 log_or_gamma 0.025 0.040 0.043 Latent field

3.2.3 Outputs

#' To-do

3.3 Investigation into large KS values

Want to create rank order lists of largest KS differences between methods:

ks_comparison <- function(ks_summary, method1, method2, n) {
  ks_method1 <- paste0("KS(", method1, ", tmbstan)")
  ks_method2 <- paste0("KS(", method2, ", tmbstan)")
  ks_summary[["KS difference"]] <- ks_summary[[ks_method1]] - ks_summary[[ks_method2]]
  ks_summary %>%
    filter(Type != "Hyper") %>%
    arrange(desc(`KS difference`)) %>%
    head(n = n)
}

3.3.1 Nodes where TMB beats aghq

ks_comparison(ks_summary, method1 = "aghq", method2 = "TMB", 10)
histogram_and_ecdf(par = "us_rho_x", i = 19)

histogram_and_ecdf(par = "ui_anc_rho_x", i = 2)

histogram_and_ecdf(par = "u_rho_x", i = 2)

3.3.2 Nodes where aghq beats TMB

ks_comparison(ks_summary, method1 = "TMB", method2 = "aghq", 10)  
histogram_and_ecdf(par = "us_alpha_xs", i = 18)

histogram_and_ecdf(par = "us_alpha_xs", i = 30)

histogram_and_ecdf(par = "u_alpha_xa", i = 10)

3.4 Correlation between KS values and ESS

Is there any correlation between the value of \(\text{KS}(\texttt{method}, \texttt{tmbstan})\) for a particular parameter and the ESS of that parameter from tmbstan output?

rhats <- bayesplot::rhat(tmbstan$mcmc$stanfit)
ess_ratio <- bayesplot::neff_ratio(tmbstan$mcmc$stanfit)
niter <- 4 * tmbstan_details$niter / tmbstan_details$nthin
ess <- ess_ratio * niter

ks_summary %>%
  pivot_longer(
    col = starts_with("KS"),
    names_to = "Method",
    values_to = "KS"
  ) %>%
  mutate(
    Method = fct_recode(Method,
      "adam" = "KS(adam, tmbstan)",
      "aghq" = "KS(aghq, tmbstan)",
      "TMB" = "KS(TMB, tmbstan)"
    )
  ) %>%
  group_by(Parameter) %>%
  mutate(
    par_num = case_when(
      max(index) > 1 ~ paste0(Parameter, "[", index, "]"),
      TRUE ~ Parameter
    )
  ) %>%
  ungroup() %>%
  left_join(data.frame(ess) %>%
    tibble::rownames_to_column("par_num")
  ) %>%
  ggplot(aes(x = ess, y = KS)) +
    geom_point(alpha = 0.5) +
    geom_smooth(method = "lm", color = "#56B4E9") +
    facet_grid(~ Method) +
    theme_minimal() +
    labs(x = "ESS", y = "KS(method, tmbstan)")
## Joining, by = "par_num"
## `geom_smooth()` using formula = 'y ~ x'